To diagonalize the angular momentum operator \(\hat{L}_{z}\)  we introduce the spherical basis functionsThe spherical wave representation of quantum fields is not very standard in QFT textbooks since scattering experiments typically are interested in states with definite linear momentum. Nevertheless, this representation is worked out in the book by W. Greiner [1]}, albeit in the Heisenberg rather than Schrödinger representation.
\(f_{klm}(r,\theta ,\varphi ) = N_{klm}\,j_{l}(kr)\, Y_{lm}(\Omega )~.\) 
